My son is 13 years old now.
Explanation
Suppose, my age [tex]=m[/tex], my father's age [tex]=f[/tex] and my son's age [tex]=s[/tex]
When I am as old as my father is now that means after [tex](f-m)[/tex] years, I will be 5 times as old as my son is now. So, the equation is.....
[tex]m+(f-m)=5s\\ \\ f= 5s ..........................(1)[/tex]
And then means after [tex](f-m)[/tex] years, my son will be 8 years older than I am now. So.....
[tex]s+(f-m)=m+8\\ \\ s+f=2m+8........................(2)[/tex]
Substituting equation (1) into equation (2), we will get.....
[tex]s+5s=2m+8\\ \\ 6s=2m+8\\ \\ 3s=m+4\\ \\ m=3s-4 .....................................(3)[/tex]
The combined ages of my father and myself are 100 years. So.....
[tex]f+m=100...............................(4)[/tex]
Now substituting [tex]f=5s[/tex] and [tex]m=3s-4[/tex] into equation (4), we will get.....
[tex]5s+(3s-4)=100\\ \\ 8s-4=100\\ \\ 8s=104\\ \\ s=\frac{104}{8}=13[/tex]
So, my son's age is 13 years now.
